# A general learning scheme for classical and quantum Ising machines

arXiv: https://arxiv.org/abs/2310.18411 · HTML: https://mlsanity.com/paper/2310.18411/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 41 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 8 of 8)

- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [QUBO Formulations for Training Machine Learning Models](https://mlsanity.com/paper/2008.02369/) (2020)
- [Efficient Optimization with Higher-Order Ising Machines](https://mlsanity.com/paper/2212.03426/) (2022)
- [Black-box optimization for integer-variable problems using Ising machines and factorization machines](https://mlsanity.com/paper/2209.01016/) (2022)
- [A Review of Machine Learning Classification Using Quantum Annealing for Real-world Applications](https://mlsanity.com/paper/2106.02964/) (2021)

## Abstract (arXiv)

An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is based on the Ising structure and can be efficiently trained using gradient descent. We provide a mathematical characterization of the training process, which is based upon optimizing a loss function whose partial derivatives are not explicitly calculated but estimated by the Ising machine itself. Moreover, we present some experimental results on the training and execution of the proposed learning model. These results point out new possibilities offered by Ising machines for different learning tasks. In particular, in the quantum realm, the quantum resources are used for both the execution and the training of the model, providing a promising perspective in quantum machine learning.